{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 9 – Up and running with TensorFlow**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 9._\n",
    "\n",
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/ageron/handson-ml/blob/master/09_up_and_running_with_tensorflow.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Warning**: this is the code for the 1st edition of the book. Please visit https://github.com/ageron/handson-ml2 for the 2nd edition code, with up-to-date notebooks using the latest library versions. In particular, the 1st edition is based on TensorFlow 1, while the 2nd edition uses TensorFlow 2, which is much simpler to use."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "try:\n",
    "    # %tensorflow_version only exists in Colab.\n",
    "    %tensorflow_version 1.x\n",
    "except Exception:\n",
    "    pass\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "def reset_graph(seed=42):\n",
    "    tf.reset_default_graph()\n",
    "    tf.set_random_seed(seed)\n",
    "    np.random.seed(seed)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"tensorflow\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating and running a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "reset_graph()\n",
    "\n",
    "x = tf.Variable(3, name=\"x\")\n",
    "y = tf.Variable(4, name=\"y\")\n",
    "f = x*x*y + y + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'add_1:0' shape=() dtype=int32>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42\n"
     ]
    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "sess.run(x.initializer)\n",
    "sess.run(y.initializer)\n",
    "result = sess.run(f)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "sess.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.Session() as sess:\n",
    "    x.initializer.run()\n",
    "    y.initializer.run()\n",
    "    result = f.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    result = f.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42\n"
     ]
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "init.run()\n",
    "result = f.eval()\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sess.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Managing graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "x1 = tf.Variable(1)\n",
    "x1.graph is tf.get_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "    x2 = tf.Variable(2)\n",
    "\n",
    "x2.graph is graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2.graph is tf.get_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "15\n"
     ]
    }
   ],
   "source": [
    "w = tf.constant(3)\n",
    "x = w + 2\n",
    "y = x + 5\n",
    "z = x * 3\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    print(y.eval())  # 10\n",
    "    print(z.eval())  # 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "15\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    y_val, z_val = sess.run([y, z])\n",
    "    print(y_val)  # 10\n",
    "    print(z_val)  # 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import fetch_california_housing\n",
    "\n",
    "reset_graph()\n",
    "\n",
    "housing = fetch_california_housing()\n",
    "m, n = housing.data.shape\n",
    "housing_data_plus_bias = np.c_[np.ones((m, 1)), housing.data]\n",
    "\n",
    "X = tf.constant(housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "XT = tf.transpose(X)\n",
    "theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), y)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    theta_value = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.7185181e+01],\n",
       "       [ 4.3633747e-01],\n",
       "       [ 9.3952334e-03],\n",
       "       [-1.0711310e-01],\n",
       "       [ 6.4479220e-01],\n",
       "       [-4.0338000e-06],\n",
       "       [-3.7813708e-03],\n",
       "       [-4.2348403e-01],\n",
       "       [-4.3721911e-01]], dtype=float32)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with pure NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.69419202e+01]\n",
      " [ 4.36693293e-01]\n",
      " [ 9.43577803e-03]\n",
      " [-1.07322041e-01]\n",
      " [ 6.45065694e-01]\n",
      " [-3.97638942e-06]\n",
      " [-3.78654265e-03]\n",
      " [-4.21314378e-01]\n",
      " [-4.34513755e-01]]\n"
     ]
    }
   ],
   "source": [
    "X = housing_data_plus_bias\n",
    "y = housing.target.reshape(-1, 1)\n",
    "theta_numpy = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "\n",
    "print(theta_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.69419202e+01]\n",
      " [ 4.36693293e-01]\n",
      " [ 9.43577803e-03]\n",
      " [-1.07322041e-01]\n",
      " [ 6.45065694e-01]\n",
      " [-3.97638942e-06]\n",
      " [-3.78654265e-03]\n",
      " [-4.21314378e-01]\n",
      " [-4.34513755e-01]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(housing.data, housing.target.reshape(-1, 1))\n",
    "\n",
    "print(np.r_[lin_reg.intercept_.reshape(-1, 1), lin_reg.coef_.T])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient Descent requires scaling the feature vectors first. We could do this using TF, but let's just use Scikit-Learn for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaled_housing_data = scaler.fit_transform(housing.data)\n",
    "scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.00000000e+00  6.60969987e-17  5.50808322e-18  6.60969987e-17\n",
      " -1.06030602e-16 -1.10161664e-17  3.44255201e-18 -1.07958431e-15\n",
      " -8.52651283e-15]\n",
      "[ 0.38915536  0.36424355  0.5116157  ... -0.06612179 -0.06360587\n",
      "  0.01359031]\n",
      "0.11111111111111005\n",
      "(20640, 9)\n"
     ]
    }
   ],
   "source": [
    "print(scaled_housing_data_plus_bias.mean(axis=0))\n",
    "print(scaled_housing_data_plus_bias.mean(axis=1))\n",
    "print(scaled_housing_data_plus_bias.mean())\n",
    "print(scaled_housing_data_plus_bias.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manually computing the gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.161542\n",
      "Epoch 100 MSE = 0.7145004\n",
      "Epoch 200 MSE = 0.56670487\n",
      "Epoch 300 MSE = 0.5555718\n",
      "Epoch 400 MSE = 0.5488112\n",
      "Epoch 500 MSE = 0.5436363\n",
      "Epoch 600 MSE = 0.5396291\n",
      "Epoch 700 MSE = 0.5365092\n",
      "Epoch 800 MSE = 0.53406775\n",
      "Epoch 900 MSE = 0.5321473\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "gradients = 2/m * tf.matmul(tf.transpose(X), error)\n",
    "training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.0685523 ],\n",
       "       [ 0.8874027 ],\n",
       "       [ 0.14401656],\n",
       "       [-0.34770882],\n",
       "       [ 0.36178368],\n",
       "       [ 0.00393811],\n",
       "       [-0.04269556],\n",
       "       [-0.6614529 ],\n",
       "       [-0.6375279 ]], dtype=float32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using autodiff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same as above except for the `gradients = ...` line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "gradients = tf.gradients(mse, [theta])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.161542\n",
      "Epoch 100 MSE = 0.71450037\n",
      "Epoch 200 MSE = 0.56670487\n",
      "Epoch 300 MSE = 0.5555718\n",
      "Epoch 400 MSE = 0.54881126\n",
      "Epoch 500 MSE = 0.5436363\n",
      "Epoch 600 MSE = 0.53962916\n",
      "Epoch 700 MSE = 0.5365092\n",
      "Epoch 800 MSE = 0.53406775\n",
      "Epoch 900 MSE = 0.5321473\n",
      "Best theta:\n",
      "[[ 2.0685523 ]\n",
      " [ 0.8874027 ]\n",
      " [ 0.14401656]\n",
      " [-0.3477088 ]\n",
      " [ 0.36178365]\n",
      " [ 0.00393811]\n",
      " [-0.04269556]\n",
      " [-0.66145283]\n",
      " [-0.6375278 ]]\n"
     ]
    }
   ],
   "source": [
    "training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How could you find the partial derivatives of the following function with regards to `a` and `b`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_func(a, b):\n",
    "    z = 0\n",
    "    for i in range(100):\n",
    "        z = a * np.cos(z + i) + z * np.sin(b - i)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.21253923284754914"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_func(0.2, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "a = tf.Variable(0.2, name=\"a\")\n",
    "b = tf.Variable(0.3, name=\"b\")\n",
    "z = tf.constant(0.0, name=\"z0\")\n",
    "for i in range(100):\n",
    "    z = a * tf.cos(z + i) + z * tf.sin(b - i)\n",
    "\n",
    "grads = tf.gradients(z, [a, b])\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compute the function at $a=0.2$ and $b=0.3$, and the partial derivatives at that point with regards to $a$ and with regards to $b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.21253741\n",
      "[-1.1388495, 0.19671397]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    print(z.eval())\n",
    "    print(sess.run(grads))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a `GradientDescentOptimizer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.161542\n",
      "Epoch 100 MSE = 0.7145004\n",
      "Epoch 200 MSE = 0.56670487\n",
      "Epoch 300 MSE = 0.5555718\n",
      "Epoch 400 MSE = 0.54881126\n",
      "Epoch 500 MSE = 0.5436363\n",
      "Epoch 600 MSE = 0.53962916\n",
      "Epoch 700 MSE = 0.5365092\n",
      "Epoch 800 MSE = 0.53406775\n",
      "Epoch 900 MSE = 0.5321473\n",
      "Best theta:\n",
      "[[ 2.0685523 ]\n",
      " [ 0.8874027 ]\n",
      " [ 0.14401656]\n",
      " [-0.3477088 ]\n",
      " [ 0.36178365]\n",
      " [ 0.00393811]\n",
      " [-0.04269556]\n",
      " [-0.66145283]\n",
      " [-0.6375278 ]]\n"
     ]
    }
   ],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a momentum optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,\n",
    "                                       momentum=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best theta:\n",
      "[[ 2.068558  ]\n",
      " [ 0.82962847]\n",
      " [ 0.11875335]\n",
      " [-0.26554456]\n",
      " [ 0.3057109 ]\n",
      " [-0.00450249]\n",
      " [-0.03932662]\n",
      " [-0.8998645 ]\n",
      " [-0.8705207 ]]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feeding data to the training algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Placeholder nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6. 7. 8.]]\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "A = tf.placeholder(tf.float32, shape=(None, 3))\n",
    "B = A + 5\n",
    "with tf.Session() as sess:\n",
    "    B_val_1 = B.eval(feed_dict={A: [[1, 2, 3]]})\n",
    "    B_val_2 = B.eval(feed_dict={A: [[4, 5, 6], [7, 8, 9]]})\n",
    "\n",
    "print(B_val_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9. 10. 11.]\n",
      " [12. 13. 14.]]\n"
     ]
    }
   ],
   "source": [
    "print(B_val_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mini-batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_epochs = 1000\n",
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_epochs = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fetch_batch(epoch, batch_index, batch_size):\n",
    "    np.random.seed(epoch * n_batches + batch_index)  # not shown in the book\n",
    "    indices = np.random.randint(m, size=batch_size)  # not shown\n",
    "    X_batch = scaled_housing_data_plus_bias[indices] # not shown\n",
    "    y_batch = housing.target.reshape(-1, 1)[indices] # not shown\n",
    "    return X_batch, y_batch\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.0703337 ],\n",
       "       [ 0.8637145 ],\n",
       "       [ 0.12255152],\n",
       "       [-0.31211877],\n",
       "       [ 0.38510376],\n",
       "       [ 0.00434168],\n",
       "       [-0.0123295 ],\n",
       "       [-0.83376896],\n",
       "       [-0.8030471 ]], dtype=float32)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Saving and restoring a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.161542\n",
      "Epoch 100 MSE = 0.7145004\n",
      "Epoch 200 MSE = 0.56670487\n",
      "Epoch 300 MSE = 0.5555718\n",
      "Epoch 400 MSE = 0.54881126\n",
      "Epoch 500 MSE = 0.5436363\n",
      "Epoch 600 MSE = 0.53962916\n",
      "Epoch 700 MSE = 0.5365092\n",
      "Epoch 800 MSE = 0.53406775\n",
      "Epoch 900 MSE = 0.5321473\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000                                                                       # not shown in the book\n",
    "learning_rate = 0.01                                                                  # not shown\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")            # not shown\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")            # not shown\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")                                      # not shown\n",
    "error = y_pred - y                                                                    # not shown\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")                                    # not shown\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)            # not shown\n",
    "training_op = optimizer.minimize(mse)                                                 # not shown\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())                                # not shown\n",
    "            save_path = saver.save(sess, \"/tmp/my_model.ckpt\")\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "    save_path = saver.save(sess, \"/tmp/my_model_final.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.0685523 ],\n",
       "       [ 0.8874027 ],\n",
       "       [ 0.14401656],\n",
       "       [-0.3477088 ],\n",
       "       [ 0.36178365],\n",
       "       [ 0.00393811],\n",
       "       [-0.04269556],\n",
       "       [-0.66145283],\n",
       "       [-0.6375278 ]], dtype=float32)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"/tmp/my_model_final.ckpt\")\n",
    "    best_theta_restored = theta.eval() # not shown in the book"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(best_theta, best_theta_restored)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to have a saver that loads and restores `theta` with a different name, such as `\"weights\"`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "saver = tf.train.Saver({\"weights\": theta})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default the saver also saves the graph structure itself in a second file with the extension `.meta`. You can use the function `tf.train.import_meta_graph()` to restore the graph structure. This function loads the graph into the default graph and returns a `Saver` that can then be used to restore the graph state (i.e., the variable values):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "# notice that we start with an empty graph.\n",
    "\n",
    "saver = tf.train.import_meta_graph(\"/tmp/my_model_final.ckpt.meta\")  # this loads the graph structure\n",
    "theta = tf.get_default_graph().get_tensor_by_name(\"theta:0\") # not shown in the book\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"/tmp/my_model_final.ckpt\")  # this restores the graph's state\n",
    "    best_theta_restored = theta.eval() # not shown in the book"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(best_theta, best_theta_restored)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that you can import a pretrained model without having to have the corresponding Python code to build the graph. This is very handy when you keep tweaking and saving your model: you can load a previously saved model without having to search for the version of the code that built it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing the graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TensorBoard is a great tool to visualize TensorFlow graphs, training curves, and much more. Our TensorFlow code will write various files in a log directory, and the TensorBoard server will regularly read these files and produce nice interactive visualizations. It can plot graphs, learning curves (i.e., how the loss evaluated on the training set or test set evolves as a function of the epoch number), profiling data to identify performance bottlenecks, and more. In short, it helps keep track of everything. Here's the overall picture:\n",
    "\n",
    "`TensorFlow writes logs to ===> log directory ===> TensorBoard reads data and displays visualizations`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to visualize different graphs, or learning curves for different training runs, we don't want the log files to get all mixed up. So we will need one log subdirectory per graph, or per run. Let's use a root log directory that we will call `tf_logs`, and a sub-directory that we will call `run-` followed by the current timestamp (you can use any other name you prefer in your own code):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "from datetime import datetime\n",
    "\n",
    "now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "root_logdir = \"tf_logs\"\n",
    "logdir = \"{}/run-{}/\".format(root_logdir, now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-20210325095200/'"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logdir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, let's create a function that will generate such a subdirectory path every time we need one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_log_subdir(run_id=None):\n",
    "    if run_id is None:\n",
    "        run_id = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "    return \"{}/run-{}/\".format(root_logdir, run_id)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's save the default graph to our log subdirectory using `tf.summary.FileWriter()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_writer = tf.summary.FileWriter(logdir, graph=tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the root log directory contains one subdirectory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['run-20210325095200']"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "os.listdir(root_logdir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And this subdirectory contains one log file (called a \"TF events\" file) for the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['events.out.tfevents.1616665937.kiwimac']"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "os.listdir(logdir)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the actual graph data may still be in the OS's file cache, so we need to `flush()` or `close()` the `FileWriter` to be sure that it's well written to disk:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, now let's start TensorBoard! It runs as a web server in a separate process, so we first need to start it. One way to do that is to run the `tensorboard` command in a terminal window. Another is to use the `%tensorboard` Jupyter extension, which takes care of starting TensorBoard, and it allows us to view TensorBoard's user interface directly within Jupyter. Let's load this extension now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The tensorboard extension is already loaded. To reload it, use:\n",
      "  %reload_ext tensorboard\n"
     ]
    }
   ],
   "source": [
    "%load_ext tensorboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's use the `%tensorboard` extension to start the TensorBoard server. We need to point it to the root log directory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-9bb87ff5937c48c\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-9bb87ff5937c48c\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! We can now visualize graphs. :)\n",
    "\n",
    "In fact, let's make this easy by creating a `save_graph()` function that will automatically create a new log subdir and save the given graph (by default `tf.get_default_graph()`) to this directory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_graph(graph=None, run_id=None):\n",
    "    if graph is None:\n",
    "        graph = tf.get_default_graph()\n",
    "    logdir = make_log_subdir(run_id)\n",
    "    file_writer = tf.summary.FileWriter(logdir, graph=graph)\n",
    "    file_writer.close()\n",
    "    return logdir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if it works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-20210325095244/'"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at TensorBoard again. Note that this will reuse the existing TensorBoard server since we're reusing the same root log directory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:00:45 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-6698e989b3fca11b\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-6698e989b3fca11b\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that you can switch between runs by picking the log subdirectory you want from the \"Run\" dropdown list (at the top left)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing Learning Curves\n",
    "\n",
    "Now let's see how to visualize learning curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "logdir = make_log_subdir()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse_summary = tf.summary.scalar('MSE', mse)\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.Session() as sess:                                                        # not shown in the book\n",
    "    sess.run(init)                                                                # not shown\n",
    "\n",
    "    for epoch in range(n_epochs):                                                 # not shown\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            if batch_index % 10 == 0:\n",
    "                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "                step = epoch * n_batches + batch_index\n",
    "                file_writer.add_summary(summary_str, step)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()                                                     # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.07033372],\n",
       "       [ 0.86371452],\n",
       "       [ 0.12255151],\n",
       "       [-0.31211874],\n",
       "       [ 0.38510373],\n",
       "       [ 0.00434168],\n",
       "       [-0.01232954],\n",
       "       [-0.83376896],\n",
       "       [-0.80304712]], dtype=float32)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at TensorBoard. Try going to the SCALARS tab:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:02:08 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-6549bb5697dded37\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-6549bb5697dded37\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Name scopes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.name_scope(\"loss\") as scope:\n",
    "    error = y_pred - y\n",
    "    mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "mse_summary = tf.summary.scalar('MSE', mse)\n",
    "\n",
    "logdir = make_log_subdir()\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best theta:\n",
      "[[ 2.07033372]\n",
      " [ 0.86371452]\n",
      " [ 0.12255151]\n",
      " [-0.31211874]\n",
      " [ 0.38510373]\n",
      " [ 0.00434168]\n",
      " [-0.01232954]\n",
      " [-0.83376896]\n",
      " [-0.80304712]]\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            if batch_index % 10 == 0:\n",
    "                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "                step = epoch * n_batches + batch_index\n",
    "                file_writer.add_summary(summary_str, step)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()\n",
    "\n",
    "file_writer.flush()\n",
    "file_writer.close()\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss/sub\n"
     ]
    }
   ],
   "source": [
    "print(error.op.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss/mse\n"
     ]
    }
   ],
   "source": [
    "print(mse.op.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a\n",
      "a_1\n",
      "param/a\n",
      "param_1/a\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "a1 = tf.Variable(0, name=\"a\")      # name == \"a\"\n",
    "a2 = tf.Variable(0, name=\"a\")      # name == \"a_1\"\n",
    "\n",
    "with tf.name_scope(\"param\"):       # name == \"param\"\n",
    "    a3 = tf.Variable(0, name=\"a\")  # name == \"param/a\"\n",
    "\n",
    "with tf.name_scope(\"param\"):       # name == \"param_1\"\n",
    "    a4 = tf.Variable(0, name=\"a\")  # name == \"param_1/a\"\n",
    "\n",
    "for node in (a1, a2, a3, a4):\n",
    "    print(node.op.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modularity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An ugly flat code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "\n",
    "w1 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights1\")\n",
    "w2 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights2\")\n",
    "b1 = tf.Variable(0.0, name=\"bias1\")\n",
    "b2 = tf.Variable(0.0, name=\"bias2\")\n",
    "\n",
    "z1 = tf.add(tf.matmul(X, w1), b1, name=\"z1\")\n",
    "z2 = tf.add(tf.matmul(X, w2), b2, name=\"z2\")\n",
    "\n",
    "relu1 = tf.maximum(z1, 0., name=\"relu1\")\n",
    "relu2 = tf.maximum(z1, 0., name=\"relu2\")  # Oops, cut&paste error! Did you spot it?\n",
    "\n",
    "output = tf.add(relu1, relu2, name=\"output\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much better, using a function to build the ReLUs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    w_shape = (int(X.get_shape()[1]), 1)\n",
    "    w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
    "    b = tf.Variable(0.0, name=\"bias\")\n",
    "    z = tf.add(tf.matmul(X, w), b, name=\"z\")\n",
    "    return tf.maximum(z, 0., name=\"relu\")\n",
    "\n",
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-relu1/'"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph(run_id=\"relu1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:04:52 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-88e2356596cb12df\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-88e2356596cb12df\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even better using name scopes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        w_shape = (int(X.get_shape()[1]), 1)                          # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")    # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                             # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                      # not shown\n",
    "        return tf.maximum(z, 0., name=\"max\")                          # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-relu2/'"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph(run_id=\"relu2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:05:43 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-57e36dbbc0430494\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-57e36dbbc0430494\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sharing Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sharing a `threshold` variable the classic way, by defining it outside of the `relu()` function then passing it as a parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X, threshold):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "threshold = tf.Variable(0.0, name=\"threshold\")\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X, threshold) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        if not hasattr(relu, \"threshold\"):\n",
    "            relu.threshold = tf.Variable(0.0, name=\"threshold\")\n",
    "        w_shape = int(X.get_shape()[1]), 1                          # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, relu.threshold, name=\"max\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "with tf.variable_scope(\"relu\"):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.variable_scope(\"relu\", reuse=True):\n",
    "    threshold = tf.get_variable(\"threshold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "with tf.variable_scope(\"relu\") as scope:\n",
    "    scope.reuse_variables()\n",
    "    threshold = tf.get_variable(\"threshold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.variable_scope(\"relu\", reuse=True):\n",
    "        threshold = tf.get_variable(\"threshold\")\n",
    "        w_shape = int(X.get_shape()[1]), 1                          # not shown\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "with tf.variable_scope(\"relu\"):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))\n",
    "relus = [relu(X) for relu_index in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-relu6/'"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph(run_id=\"relu6\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:06:21 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-f55ce8541b1e56b0\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-f55ce8541b1e56b0\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.variable_scope(\"relu\"):\n",
    "        threshold = tf.get_variable(\"threshold\", shape=(), initializer=tf.constant_initializer(0.0))\n",
    "        w_shape = (int(X.get_shape()[1]), 1)\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
    "        b = tf.Variable(0.0, name=\"bias\")\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "with tf.variable_scope(\"\", default_name=\"\") as scope:\n",
    "    first_relu = relu(X)     # create the shared variable\n",
    "    scope.reuse_variables()  # then reuse it\n",
    "    relus = [first_relu] + [relu(X) for i in range(4)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-relu8/'"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph(run_id=\"relu8\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:06:45 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-41cda150228bada\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-41cda150228bada\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))\n",
    "    w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book\n",
    "    w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "    b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "    z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "    return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = []\n",
    "for relu_index in range(5):\n",
    "    with tf.variable_scope(\"relu\", reuse=(relu_index >= 1)) as scope:\n",
    "        relus.append(relu(X))\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tf_logs/run-relu9/'"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_graph(run_id=\"relu9\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Reusing TensorBoard on port 6006 (pid 43590), started 0:07:06 ago. (Use '!kill 43590' to kill it.)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "      <iframe id=\"tensorboard-frame-5f6a27b4563df923\" width=\"100%\" height=\"800\" frameborder=\"0\">\n",
       "      </iframe>\n",
       "      <script>\n",
       "        (function() {\n",
       "          const frame = document.getElementById(\"tensorboard-frame-5f6a27b4563df923\");\n",
       "          const url = new URL(\"/\", window.location);\n",
       "          url.port = 6006;\n",
       "          frame.src = url;\n",
       "        })();\n",
       "      </script>\n",
       "  "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extra material"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0: my_scope/x\n",
      "x1: my_scope/x_1\n",
      "x2: my_scope/x_2\n",
      "x3: my_scope/x\n",
      "x4: my_scope_1/x\n",
      "x5: my_scope/x\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "with tf.variable_scope(\"my_scope\"):\n",
    "    x0 = tf.get_variable(\"x\", shape=(), initializer=tf.constant_initializer(0.))\n",
    "    x1 = tf.Variable(0., name=\"x\")\n",
    "    x2 = tf.Variable(0., name=\"x\")\n",
    "\n",
    "with tf.variable_scope(\"my_scope\", reuse=True):\n",
    "    x3 = tf.get_variable(\"x\")\n",
    "    x4 = tf.Variable(0., name=\"x\")\n",
    "\n",
    "with tf.variable_scope(\"\", default_name=\"\", reuse=True):\n",
    "    x5 = tf.get_variable(\"my_scope/x\")\n",
    "\n",
    "print(\"x0:\", x0.op.name)\n",
    "print(\"x1:\", x1.op.name)\n",
    "print(\"x2:\", x2.op.name)\n",
    "print(\"x3:\", x3.op.name)\n",
    "print(\"x4:\", x4.op.name)\n",
    "print(\"x5:\", x5.op.name)\n",
    "print(x0 is x3 and x3 is x5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first `variable_scope()` block first creates the shared variable `x0`, named `my_scope/x`. For all operations other than shared variables (including non-shared variables), the variable scope acts like a regular name scope, which is why the two variables `x1` and `x2` have a name with a prefix `my_scope/`. Note however that TensorFlow makes their names unique by adding an index: `my_scope/x_1` and `my_scope/x_2`.\n",
    "\n",
    "The second `variable_scope()` block reuses the shared variables in scope `my_scope`, which is why `x0 is x3`. Once again, for all operations other than shared variables it acts as a named scope, and since it's a separate block from the first one, the name of the scope is made unique by TensorFlow (`my_scope_1`) and thus the variable `x4` is named `my_scope_1/x`.\n",
    "\n",
    "The third block shows another way to get a handle on the shared variable `my_scope/x` by creating a `variable_scope()` at the root scope (whose name is an empty string), then calling `get_variable()` with the full name of the shared variable (i.e. `\"my_scope/x\"`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[b'Do' b'you' b'want' b'some' b'caf\\xc3\\xa9?']\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "text = np.array(\"Do you want some café?\".split())\n",
    "text_tensor = tf.constant(text)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    print(text_tensor.eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autodiff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: the autodiff content was moved to the [extra_autodiff.ipynb](extra_autodiff.ipynb) notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Logistic Regression with Mini-Batch Gradient Descent using TensorFlow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's create the moons dataset using Scikit-Learn's `make_moons()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "m = 1000\n",
    "X_moons, y_moons = make_moons(m, noise=0.1, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a peek at the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i7qQkM9ZfgJHABygh0YrCmHsnarJaERDAR5pGet263F6vntsktO/4cYL27EHr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\nrQDSUMbD3M2dNI65HtK/SCf90nSbN+CQO8ijSRmGaEQoLTArzqTN1Jy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4/ADDzh+GvEBS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d104cef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_moons[y_moons == 1, 0], X_moons[y_moons == 1, 1], 'go', label=\"Positive\")\n",
    "plt.plot(X_moons[y_moons == 0, 0], X_moons[y_moons == 0, 1], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We must not forget to add an extra bias feature ($x_0 = 1$) to every instance. For this, we just need to add a column full of 1s on the left of the input matrix $\\mathbf{X}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_moons_with_bias = np.c_[np.ones((m, 1)), X_moons]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.05146968,  0.44419863],\n",
       "       [ 1.        ,  1.03201691, -0.41974116],\n",
       "       [ 1.        ,  0.86789186, -0.25482711],\n",
       "       [ 1.        ,  0.288851  , -0.44866862],\n",
       "       [ 1.        , -0.83343911,  0.53505665]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_moons_with_bias[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good. Now let's reshape `y_train` to make it a column vector (i.e. a 2D array with a single column):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_moons_column_vector = y_moons.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's split the data into a training set and a test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "test_size = int(m * test_ratio)\n",
    "X_train = X_moons_with_bias[:-test_size]\n",
    "X_test = X_moons_with_bias[-test_size:]\n",
    "y_train = y_moons_column_vector[:-test_size]\n",
    "y_test = y_moons_column_vector[-test_size:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, now let's create a small function to generate training batches. In this implementation we will just pick random instances from the training set for each batch. This means that a single batch may contain the same instance multiple times, and also a single epoch may not cover all the training instances (in fact it will generally cover only about two thirds of the instances). However, in practice this is not an issue and it simplifies the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_batch(X_train, y_train, batch_size):\n",
    "    rnd_indices = np.random.randint(0, len(X_train), batch_size)\n",
    "    X_batch = X_train[rnd_indices]\n",
    "    y_batch = y_train[rnd_indices]\n",
    "    return X_batch, y_batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at a small batch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  1.93189866,  0.13158788],\n",
       "       [ 1.        ,  1.07172763,  0.13482039],\n",
       "       [ 1.        , -1.01148674, -0.04686381],\n",
       "       [ 1.        ,  0.02201868,  0.19079139],\n",
       "       [ 1.        , -0.98941204,  0.02473116]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_batch, y_batch = random_batch(X_train, y_train, 5)\n",
    "X_batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [0],\n",
       "       [0],\n",
       "       [1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now that the data is ready to be fed to the model, we need to build that model. Let's start with a simple implementation, then we will add all the bells and whistles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's reset the default graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reset_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _moons_ dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_inputs = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the Logistic Regression model. As we saw in chapter 4, this model first computes a weighted sum of the inputs (just like the Linear Regression model), and then it applies the sigmoid function to the result, which gives us the estimated probability for the positive class:\n",
    "\n",
    "$\\hat{p} = h_\\boldsymbol{\\theta}(\\mathbf{x}) = \\sigma(\\boldsymbol{\\theta}^T \\mathbf{x})$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that $\\boldsymbol{\\theta}$ is the parameter vector, containing the bias term $\\theta_0$ and the weights $\\theta_1, \\theta_2, \\dots, \\theta_n$. The input vector $\\mathbf{x}$ contains a constant term $x_0 = 1$, as well as all the input features $x_1, x_2, \\dots, x_n$.\n",
    "\n",
    "Since we want to be able to make predictions for multiple instances at a time, we will use an input matrix $\\mathbf{X}$ rather than a single input vector. The $i^{th}$ row will contain the transpose of the $i^{th}$ input vector $(\\mathbf{x}^{(i)})^T$. It is then possible to estimate the probability that each instance belongs to the positive class using the following equation:\n",
    "\n",
    "$ \\hat{\\mathbf{p}} = \\sigma(\\mathbf{X} \\boldsymbol{\\theta})$\n",
    "\n",
    "That's all we need to build the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n_inputs + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "logits = tf.matmul(X, theta, name=\"logits\")\n",
    "y_proba = 1 / (1 + tf.exp(-logits))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, TensorFlow has a nice function `tf.sigmoid()` that we can use to simplify the last line of the previous code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_proba = tf.sigmoid(logits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression:\n",
    "\n",
    "$J(\\boldsymbol{\\theta}) = -\\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{\\left[ y^{(i)} \\log\\left(\\hat{p}^{(i)}\\right) + (1 - y^{(i)}) \\log\\left(1 - \\hat{p}^{(i)}\\right)\\right]}$\n",
    "\n",
    "One option is to implement it ourselves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 1e-7  # to avoid an overflow when computing the log\n",
    "loss = -tf.reduce_mean(y * tf.log(y_proba + epsilon) + (1 - y) * tf.log(1 - y_proba + epsilon))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we might as well use TensorFlow's `tf.losses.log_loss()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "loss = tf.losses.log_loss(y, y_proba)  # uses epsilon = 1e-7 by default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest is pretty standard: let's create the optimizer and tell it to minimize the cost function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.01\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All we need now (in this minimal version) is the variable initializer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we are ready to train the model and use it for predictions!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's really nothing special about this code, it's virtually the same as the one we used earlier for Linear Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 \tLoss: 0.792602\n",
      "Epoch: 100 \tLoss: 0.343463\n",
      "Epoch: 200 \tLoss: 0.30754\n",
      "Epoch: 300 \tLoss: 0.292889\n",
      "Epoch: 400 \tLoss: 0.285336\n",
      "Epoch: 500 \tLoss: 0.280478\n",
      "Epoch: 600 \tLoss: 0.278083\n",
      "Epoch: 700 \tLoss: 0.276154\n",
      "Epoch: 800 \tLoss: 0.27552\n",
      "Epoch: 900 \tLoss: 0.274912\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 1000\n",
    "batch_size = 50\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = random_batch(X_train, y_train, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        loss_val = loss.eval({X: X_test, y: y_test})\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch:\", epoch, \"\\tLoss:\", loss_val)\n",
    "\n",
    "    y_proba_val = y_proba.eval(feed_dict={X: X_test, y: y_test})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: we don't use the epoch number when generating batches, so we could just have a single `for` loop rather than 2 nested `for` loops, but it's convenient to think of training time in terms of number of epochs (i.e., roughly the number of times the algorithm went through the training set)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each instance in the test set, `y_proba_val` contains the estimated probability that it belongs to the positive class, according to the model. For example, here are the first 5 estimated probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.54895616],\n",
       "       [ 0.70724374],\n",
       "       [ 0.51900256],\n",
       "       [ 0.9911136 ],\n",
       "       [ 0.50859052]], dtype=float32)"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba_val[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To classify each instance, we can go for maximum likelihood: classify as positive any instance whose estimated probability is greater or equal to 0.5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [ True]], dtype=bool)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = (y_proba_val >= 0.5)\n",
    "y_pred[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the use case, you may want to choose a different threshold than 0.5: make it higher if you want high precision (but lower recall), and make it lower if you want high recall (but lower precision). See chapter 3 for more details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compute the model's precision and recall:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86274509803921573"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score, recall_score\n",
    "\n",
    "precision_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.88888888888888884"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot these predictions to see what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o6W/luUSgtKyUgfcOZFH6IoqzilmUvoiB9w6ktKw02qLFHuFolki8qGczh0R+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\nykEQBEHwQpSDIAiC4MX/B4BXNRO7H//+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d0e11f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector\n",
    "plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label=\"Positive\")\n",
    "plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, that looks pretty bad, doesn't it? But let's not forget that the Logistic Regression model has a linear decision boundary, so this is actually close to the best we can do with this model (unless we add more features, as we will show in a second)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's start over, but this time we will add all the bells and whistles, as listed in the exercise:\n",
    "* Define the graph within a `logistic_regression()` function that can be reused easily.\n",
    "* Save checkpoints using a `Saver` at regular intervals during training, and save the final model at the end of training.\n",
    "* Restore the last checkpoint upon startup if training was interrupted.\n",
    "* Define the graph using nice scopes so the graph looks good in TensorBoard.\n",
    "* Add summaries to visualize the learning curves in TensorBoard.\n",
    "* Try tweaking some hyperparameters such as the learning rate or the mini-batch size and look at the shape of the learning curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start, we will add 4 more features to the inputs: ${x_1}^2$, ${x_2}^2$, ${x_1}^3$ and ${x_2}^3$. This was not part of the exercise, but it will demonstrate how adding features can improve the model. We will do this manually, but you could also add them using `sklearn.preprocessing.PolynomialFeatures`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train_enhanced = np.c_[X_train,\n",
    "                         np.square(X_train[:, 1]),\n",
    "                         np.square(X_train[:, 2]),\n",
    "                         X_train[:, 1] ** 3,\n",
    "                         X_train[:, 2] ** 3]\n",
    "X_test_enhanced = np.c_[X_test,\n",
    "                        np.square(X_test[:, 1]),\n",
    "                        np.square(X_test[:, 2]),\n",
    "                        X_test[:, 1] ** 3,\n",
    "                        X_test[:, 2] ** 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what the \"enhanced\" training set looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.00000000e+00,  -5.14696757e-02,   4.44198631e-01,\n",
       "          2.64912752e-03,   1.97312424e-01,  -1.36349734e-04,\n",
       "          8.76459084e-02],\n",
       "       [  1.00000000e+00,   1.03201691e+00,  -4.19741157e-01,\n",
       "          1.06505890e+00,   1.76182639e-01,   1.09915879e+00,\n",
       "         -7.39511049e-02],\n",
       "       [  1.00000000e+00,   8.67891864e-01,  -2.54827114e-01,\n",
       "          7.53236288e-01,   6.49368582e-02,   6.53727646e-01,\n",
       "         -1.65476722e-02],\n",
       "       [  1.00000000e+00,   2.88850997e-01,  -4.48668621e-01,\n",
       "          8.34348982e-02,   2.01303531e-01,   2.41002535e-02,\n",
       "         -9.03185778e-02],\n",
       "       [  1.00000000e+00,  -8.33439108e-01,   5.35056649e-01,\n",
       "          6.94620746e-01,   2.86285618e-01,  -5.78924095e-01,\n",
       "          1.53179024e-01]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_enhanced[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, next let's reset the default graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reset_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's define the `logistic_regression()` function to create the graph. We will leave out the definition of the inputs `X` and the targets `y`. We could include them here, but leaving them out will make it easier to use this function in a wide range of use cases (e.g. perhaps we will want to add some preprocessing steps for the inputs before we feed them to the Logistic Regression model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def logistic_regression(X, y, initializer=None, seed=42, learning_rate=0.01):\n",
    "    n_inputs_including_bias = int(X.get_shape()[1])\n",
    "    with tf.name_scope(\"logistic_regression\"):\n",
    "        with tf.name_scope(\"model\"):\n",
    "            if initializer is None:\n",
    "                initializer = tf.random_uniform([n_inputs_including_bias, 1], -1.0, 1.0, seed=seed)\n",
    "            theta = tf.Variable(initializer, name=\"theta\")\n",
    "            logits = tf.matmul(X, theta, name=\"logits\")\n",
    "            y_proba = tf.sigmoid(logits)\n",
    "        with tf.name_scope(\"train\"):\n",
    "            loss = tf.losses.log_loss(y, y_proba, scope=\"loss\")\n",
    "            optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "            training_op = optimizer.minimize(loss)\n",
    "            loss_summary = tf.summary.scalar('log_loss', loss)\n",
    "        with tf.name_scope(\"init\"):\n",
    "            init = tf.global_variables_initializer()\n",
    "        with tf.name_scope(\"save\"):\n",
    "            saver = tf.train.Saver()\n",
    "    return y_proba, loss, training_op, loss_summary, init, saver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a little function to get the name of the log directory to save the summaries for Tensorboard:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from datetime import datetime\n",
    "\n",
    "def log_dir(prefix=\"\"):\n",
    "    now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "    root_logdir = \"tf_logs\"\n",
    "    if prefix:\n",
    "        prefix += \"-\"\n",
    "    name = prefix + \"run-\" + now\n",
    "    return \"{}/{}/\".format(root_logdir, name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's create the graph, using the `logistic_regression()` function. We will also create the `FileWriter` to save the summaries to the log directory for Tensorboard:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = 2 + 4\n",
    "logdir = log_dir(\"logreg\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "\n",
    "y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(X, y)\n",
    "\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At last we can train the model! We will start by checking whether a previous training session was interrupted, and if so we will load the checkpoint and continue training from the epoch number we saved. In this example we just save the epoch number to a separate file, but in chapter 11 we will see how to store the training step directly as part of the model, using a non-trainable variable called `global_step` that we pass to the optimizer's `minimize()` method.\n",
    "\n",
    "You can try interrupting training to verify that it does indeed restore the last checkpoint when you start it again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 \tLoss: 0.629985\n",
      "Epoch: 500 \tLoss: 0.161224\n",
      "Epoch: 1000 \tLoss: 0.119032\n",
      "Epoch: 1500 \tLoss: 0.0973292\n",
      "Epoch: 2000 \tLoss: 0.0836979\n",
      "Epoch: 2500 \tLoss: 0.0743758\n",
      "Epoch: 3000 \tLoss: 0.0675021\n",
      "Epoch: 3500 \tLoss: 0.0622069\n",
      "Epoch: 4000 \tLoss: 0.0580268\n",
      "Epoch: 4500 \tLoss: 0.054563\n",
      "Epoch: 5000 \tLoss: 0.0517083\n",
      "Epoch: 5500 \tLoss: 0.0492377\n",
      "Epoch: 6000 \tLoss: 0.0471673\n",
      "Epoch: 6500 \tLoss: 0.0453766\n",
      "Epoch: 7000 \tLoss: 0.0438187\n",
      "Epoch: 7500 \tLoss: 0.0423742\n",
      "Epoch: 8000 \tLoss: 0.0410892\n",
      "Epoch: 8500 \tLoss: 0.0399709\n",
      "Epoch: 9000 \tLoss: 0.0389202\n",
      "Epoch: 9500 \tLoss: 0.0380107\n",
      "Epoch: 10000 \tLoss: 0.0371557\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10001\n",
    "batch_size = 50\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "checkpoint_path = \"/tmp/my_logreg_model.ckpt\"\n",
    "checkpoint_epoch_path = checkpoint_path + \".epoch\"\n",
    "final_model_path = \"./my_logreg_model\"\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    if os.path.isfile(checkpoint_epoch_path):\n",
    "        # if the checkpoint file exists, restore the model and load the epoch number\n",
    "        with open(checkpoint_epoch_path, \"rb\") as f:\n",
    "            start_epoch = int(f.read())\n",
    "        print(\"Training was interrupted. Continuing at epoch\", start_epoch)\n",
    "        saver.restore(sess, checkpoint_path)\n",
    "    else:\n",
    "        start_epoch = 0\n",
    "        sess.run(init)\n",
    "\n",
    "    for epoch in range(start_epoch, n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})\n",
    "        file_writer.add_summary(summary_str, epoch)\n",
    "        if epoch % 500 == 0:\n",
    "            print(\"Epoch:\", epoch, \"\\tLoss:\", loss_val)\n",
    "            saver.save(sess, checkpoint_path)\n",
    "            with open(checkpoint_epoch_path, \"wb\") as f:\n",
    "                f.write(b\"%d\" % (epoch + 1))\n",
    "\n",
    "    saver.save(sess, final_model_path)\n",
    "    y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})\n",
    "    os.remove(checkpoint_epoch_path)\n",
    "\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we can make predictions by just classifying as positive all the instances whose estimated probability is greater or equal to 0.5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = (y_proba_val >= 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97979797979797978"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97979797979797978"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yeiSL5vpNOhscnoN8OIO7zDy9SZfZZ7TKQWorJYB0r5E0dfbUesUA0BTKzy9n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\nOdVQChswFEMrkrLvkgFRDkL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d29e95f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector\n",
    "plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label=\"Positive\")\n",
    "plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that's much, much better! Apparently the new features really helped a lot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's open tensorboard, find the latest run and look at the learning curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "%tensorboard --logdir {root_logdir}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can play around with the hyperparameters (e.g. the `batch_size` or the `learning_rate`) and run training again and again, comparing the learning curves. You can even automate this process by implementing grid search or randomized search. Below is a simple implementation of a randomized search on both the batch size and the learning rate. For the sake of simplicity, the checkpoint mechanism was removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "  logdir: tf_logs/logreg-run-20170606195328/\n",
      "  batch size: 19\n",
      "  learning_rate: 0.00443037524522\n",
      "  training: .....................\n",
      "  precision: 0.979797979798\n",
      "  recall: 0.979797979798\n",
      "Iteration 1\n",
      "  logdir: tf_logs/logreg-run-20170606195605/\n",
      "  batch size: 80\n",
      "  learning_rate: 0.00178264971514\n",
      "  training: .....................\n",
      "  precision: 0.969696969697\n",
      "  recall: 0.969696969697\n",
      "Iteration 2\n",
      "  logdir: tf_logs/logreg-run-20170606195646/\n",
      "  batch size: 73\n",
      "  learning_rate: 0.00203228544324\n",
      "  training: .....................\n",
      "  precision: 0.969696969697\n",
      "  recall: 0.969696969697\n",
      "Iteration 3\n",
      "  logdir: tf_logs/logreg-run-20170606195730/\n",
      "  batch size: 6\n",
      "  learning_rate: 0.00449152382514\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 4\n",
      "  logdir: tf_logs/logreg-run-20170606200523/\n",
      "  batch size: 24\n",
      "  learning_rate: 0.0796323472178\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 5\n",
      "  logdir: tf_logs/logreg-run-20170606200726/\n",
      "  batch size: 75\n",
      "  learning_rate: 0.000463425058329\n",
      "  training: .....................\n",
      "  precision: 0.912621359223\n",
      "  recall: 0.949494949495\n",
      "Iteration 6\n",
      "  logdir: tf_logs/logreg-run-20170606200810/\n",
      "  batch size: 86\n",
      "  learning_rate: 0.0477068184194\n",
      "  training: .....................\n",
      "  precision: 0.98\n",
      "  recall: 0.989898989899\n",
      "Iteration 7\n",
      "  logdir: tf_logs/logreg-run-20170606200851/\n",
      "  batch size: 87\n",
      "  learning_rate: 0.000169404470952\n",
      "  training: .....................\n",
      "  precision: 0.888888888889\n",
      "  recall: 0.808080808081\n",
      "Iteration 8\n",
      "  logdir: tf_logs/logreg-run-20170606200932/\n",
      "  batch size: 61\n",
      "  learning_rate: 0.0417146119941\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 9\n",
      "  logdir: tf_logs/logreg-run-20170606201026/\n",
      "  batch size: 92\n",
      "  learning_rate: 0.000107429229684\n",
      "  training: .....................\n",
      "  precision: 0.882352941176\n",
      "  recall: 0.757575757576\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import reciprocal\n",
    "\n",
    "n_search_iterations = 10\n",
    "\n",
    "for search_iteration in range(n_search_iterations):\n",
    "    batch_size = np.random.randint(1, 100)\n",
    "    learning_rate = reciprocal(0.0001, 0.1).rvs(random_state=search_iteration)\n",
    "\n",
    "    n_inputs = 2 + 4\n",
    "    logdir = log_dir(\"logreg\")\n",
    "    \n",
    "    print(\"Iteration\", search_iteration)\n",
    "    print(\"  logdir:\", logdir)\n",
    "    print(\"  batch size:\", batch_size)\n",
    "    print(\"  learning_rate:\", learning_rate)\n",
    "    print(\"  training: \", end=\"\")\n",
    "\n",
    "    reset_graph()\n",
    "\n",
    "    X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "    y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "\n",
    "    y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(\n",
    "        X, y, learning_rate=learning_rate)\n",
    "\n",
    "    file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())\n",
    "\n",
    "    n_epochs = 10001\n",
    "    n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "    final_model_path = \"./my_logreg_model_%d\" % search_iteration\n",
    "\n",
    "    with tf.Session() as sess:\n",
    "        sess.run(init)\n",
    "\n",
    "        for epoch in range(n_epochs):\n",
    "            for batch_index in range(n_batches):\n",
    "                X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)\n",
    "                sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "            loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})\n",
    "            file_writer.add_summary(summary_str, epoch)\n",
    "            if epoch % 500 == 0:\n",
    "                print(\".\", end=\"\")\n",
    "\n",
    "        saver.save(sess, final_model_path)\n",
    "\n",
    "        print()\n",
    "        y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})\n",
    "        y_pred = (y_proba_val >= 0.5)\n",
    "        \n",
    "        print(\"  precision:\", precision_score(y_test, y_pred))\n",
    "        print(\"  recall:\", recall_score(y_test, y_pred))\n",
    "\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `reciprocal()` function from SciPy's `stats` module returns a random distribution that is commonly used when you have no idea of the optimal scale of a hyperparameter. See the exercise solutions for chapter 2 for more details. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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